Mobile impurity interacting with a Hubbard chain and the role of Friedel oscillations

TL;DR

This paper investigates the behavior of a mobile impurity in a small one-dimensional fermionic Hubbard system, revealing phase separation phenomena and Friedel oscillation effects on impurity density patterns.

Contribution

It introduces an exact diagonalization study of impurity interactions in a Hubbard chain, highlighting novel phase separation and oscillatory behaviors due to Friedel oscillations.

Findings

Impurity exhibits phase separation with fermionic bath.

Attractive impurity can phase separate with holes.

Impurity density shows oscillations from Friedel effects.

Abstract

This work examines a mobile impurity interacting with a bath of a few spin-$\uparrow$ and spin-$\downarrow$ fermions in a small one-dimensional open lattice system. We study ground-state properties using the exact diagonalization method, where the system is modeled by a three-component Fermi Hubbard Hamiltonian. We find that in addition to the standard phase separation between a strongly repulsive impurity and the bath, a strongly-attractive impurity also phase separates with the fermionic holes. Furthermore, we find that the impurity can show an oscillatory pattern in its density for intermediate bath-impurity interactions, which are induced by Friedel oscillations in the fermionic bath. This rich behavior of the impurity could be probed with fermionic ultracold mixtures in optical lattices.